Most interesting biological phenomena occur when cells or biological systems are undergoing change rather than when they are at equilibrium or steady-state. Quantitating the dynamics of a biological process is important to fully understanding it. A biological process typically is composed of a series of interrelated chemical reactions whose rates may be described mathematically by coupled differential equations. Quantitative kinetic models were developed for the following biological processes: (1) cellular trafficking of epidermal growth factor (EGF) and its receptor. Models were tested by fitting them to radiolabeled ligand and receptor data. Estimates for rate constants of binding, internalization and degradation were obtained. The models were also examined with respect to their ability to predict the pharmacodynamics of iodine-125-EGF toxicity in cultures of neoplastic cells expressing the EGF receptor. (2) in vivo accumulation of transferrin in liver and solid tumors. A kinetic model was developed that describes the rate of radiolabeled transferrin uptake in low- and high- permeability tissues and receptor binding in the presence of endogenous transferrin. Model simulations under a wide range of parameter values illustrates the difficulties of obtaining high tumor to normal ratios on a time-scale commensurate with the half-life of positron emitting radionuclides such as fluorine- 18. (3) kinetics of HIV infection. As knowledge of HIV biology increases, mathematical models of the disease and treatment processes are being improved. Quantitative characterization of the dynamics of HIV infection is critically important to the design of antiretroviral drug treatment protocols. (This is a continuation of Intramural Research Project Z01-RR-10490-01 BEI.)